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A100284 Expansion of (1-4*x-x^2)/((1-x)*(1-4*x-5*x^2)). 4
1, 1, 5, 21, 105, 521, 2605, 13021, 65105, 325521, 1627605, 8138021, 40690105, 203450521, 1017252605, 5086263021, 25431315105, 127156575521, 635782877605, 3178914388021, 15894571940105, 79472859700521, 397364298502605 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Binomial transform of A054881.
Binomial transform of A179607. - Johannes W. Meijer, Aug 01 2010
LINKS
FORMULA
a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3).
a(n) = (1/6)*(3 + 5^n + 2*(-1)^n).
E.g.f.: (1/6)*(exp(5*x) + 3*exp(x) + 2*exp(-x)). - G. C. Greubel, Feb 06 2023
MATHEMATICA
CoefficientList[Series[(1-4x-x^2)/((1-x)(1-4x-5x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, 1, -5}, {1, 1, 5}, 30] (* Harvey P. Dale, Apr 01 2013 *)
PROG
(Magma) [(5^n +2*(-1)^n +3)/6: n in [0..40]]; // G. C. Greubel, Feb 06 2023
(SageMath)
def A100284(n): return (1/6)*(5^n +1 +4*((n+1)%2))
[A100284(n) for n in range(41)] # G. C. Greubel, Feb 06 2023
CROSSREFS
Sequence in context: A280623 A203154 A097175 * A337168 A341853 A260845
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 11 2004
STATUS
approved

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)